Microtubule bundling and nested buckling drive stripe formation in polymerizing tubulin solutions

Abstract

Various mechanisms govern pattern formation in chemical and biological reaction systems, giving rise to structures with distinct morphologies and physical properties. The self-organization of polymerizing microtubules (MTs) is of particular interest because of its implications for biological function. We report a study of the microscopic structure and properties of the striped patterns that spontaneously form in polymerizing tubulin solutions and propose a mechanism driving this assembly. Microscopic observations reveal that the pattern comprises wave-like MT bundles. The retardance of the solution and the fluorescence intensity of labeled MTs vary periodically in space, suggesting a coincident periodic variation in MT alignment and density. This wave-like structure forms through the development and coordinated buckling of initially aligned MT bundles. Both static magnetic fields and convective flow can induce the initial alignment. The nesting of the buckled MT bundles gives rise to density variations that are in quantitative accord with the data. We further propose that the buckling wavelength is selected by a balance between the bending energy of the bundles and the elastic energy of the MT network surrounding them. These studies reveal a unique physical chemical mechanism by which mechanical buckling couples with protein polymerization to produce macroscopic patterns. Self-organization of this type may be important to the formation of certain biological structures.

Pattern formation through chemical reaction and diffusion has been of great interest to biologists since Turing (1) proposed it as an adequate mechanism to account for the main phenomena of morphogenesis. There have been numerous studies of reaction–diffusion systems that start from an initially homogeneous state and develop spatial and temporal oscillations in their reactant concentrations (2, 3). In this work, we present a study of the spontaneous formation of striped patterns in polymerizing solutions of a cytoskeleton protein, tubulin. Tubulin consists of protein heterodimers that longitudinally associate with one another to form protofilaments that constitute the cylindrical microtubule (MT) wall. The polymerizing tubulin solutions develop spatial oscillations in MT concentration (4) similar to reaction diffusion systems. However, our microscopic observations and quantitative analyses of the spatial variations of retardance and fluorescence intensity indicate that a different mechanism leads to the observed concentration undulation.

The MT system has served as a model for studying pattern formation by biomolecules (5). Many fundamental cellular processes require the correct organization of MTs within a cell. They organize into the spindles and asters essential for mitosis (6) and parallel arrays and stripes that direct early processes in embryogenesis (7, 8). Efforts to elucidate the mechanisms underlying the formation of these structures have led to many in vitro studies of MT organization. One of the recent studies (9) has revealed that mixed solutions of MTs and molecular motors can self-organize into a wide variety of structures, including asters, through their mechanical interactions. Of particular relevance here are the striped birefringent patterns that spontaneously form in MT solutions without motors. Hitt et al. (10) attributed these patterns to the formation of liquid crystalline domains. Tabony (11), on the other hand, proposed a reaction–diffusion-based mechanism, suggesting that reaction–diffusion could account qualitatively for the concentration variations (4) and the sensitivity of the patterns to symmetry-breaking perturbations such as gravity and magnetic fields (12).

We present results regarding the structural basis for the birefringent stripes and the origin of the spatial concentration oscillations in the striped patterns through a series of microscopic investigations, including phase-contrast, fluorescence, and quantitative polarized light microscopy. These results suggest a microscopic picture of MTs aligning along wave-like MT bundles, which gives rise to a continuous variation of the slow axis direction (orientation of MT bundles). Measurements of the magnitude of retardance and fluorescence intensity reflect a periodic variation in MT density in the stripes, which is quantitatively accounted for by the nesting of buckled bundles. We propose a two-stage mechanism for the stripe formation: polymerizing MTs align uniformly along the direction of external magnetic fields or convective flow and form bundles in the early stage; the bundles grow because of the elongation of constituent MTs and eventually buckle and nest into a wave-like shape in the later stage. We suggest that the bundles buckle to relieve compressional stress that builds up because of internal MT polymerization forces. The buckling mode selected minimizes the accompanying increases in the bundle bending energy and the elastic energy of a background network of dispersed MTs. These results show that mechanical instability coupled with the biochemical process of polymerization drives the striped pattern formation.

Results and Analyses

Birefringent Stripes Form Out of Uniformly Aligned MTs.

A representative example of the birefringent stripes that emerge in polymerizing MT solutions is shown in Fig. 1. An applied vertical 9-Tesla static magnetic field aligned the MTs during the first 5 min after the onset of polymerization as shown in Fig. 1A. Then the sample was placed in a 30°C room. The birefringent stripes oriented roughly perpendicular to the original MT alignment direction as shown in Fig. 1B. Time-lapse records of this stripe-forming process are shown in Movie 1, which is published as supporting information on the PNAS web site. Once formed, the pattern is stable for at least 24 h. Stripes also form out of MTs initially aligned by convective flow (see Fig. 2). Steric constraints imposed by the high aspect ratio of the cuvettes may also induce some extent of alignment. In experiments in which polymerization was initiated in the absence of magnetic fields or substantial convective flow, discrete striped domains appeared near the walls of the cuvette (data not shown), indicating an initial alignment of MTs by steric constraints.

Fig. 1.

Pattern development of polymerizing 5 mg/ml MTs after initial alignment by a 9-tesla vertical static magnetic field for 5 min. The images were taken between crossed polarizers with the long axis of the cuvette (8 mm wide, 0.4 mm thick) at 45° with respect to the polarizing directions of the polarizers. (A) Image after 5 min of polymerization in the magnetic field. Notice that the solution appears brighter than the background region outside the meniscus, which has no birefringence. Rotating the cuvette by 45° changes the image to dark (data not shown), indicating that MTs are aligned in the magnetic field direction. (B) The same sample imaged 30 min after initiation of polymerization, showing formation of stripes that are aligned predominantly in the direction perpendicular to the direction of initial bulk alignment.

Fig. 2.

Successive frames of a typical phase-contrast movie (Movie 2) showing buckling of MT bundles. The contrast of the images here was enhanced for better visualization. Tubulin solution (8 mg/ml) in a 40 × 10 × 1-mm cuvette was prepared as described in Materials and Methods. The sample was subjected to convective flow (induced by asymmetrical thermal contacts between the two edges of the cuvette with a water bath-warmed aluminum holder) for the first 9 min, and then the cuvette was laid flat on the microscope stage at 30°C.

MTs Form Bundles, and the Bundles Buckle to Form a Wave-Like Structure.

The sequence of phase-contrast microscopy images shown in Fig. 2 reveals the morphology of the MTs. At 10 min, striations with a gradual undulation are apparent. This undulation becomes stronger with time until its amplitude is comparable to its spatial period. We identify the striations as bundled MTs because single MTs are unresolvable with this technique. MT bundles are also clearly recognizable in fluorescence and PolScope images of samples taken out from cuvettes that contain striped patterns, as shown in Fig. 3. MT clouds instead of bundles were observed in samples in which the stripes did not form. This result suggests that MT bundling is necessary for the formation of the striped patterns. Thus, initially aligned MTs form bundles and buckle coherently with their neighbors to form a wave-like pattern. The pattern formed out of a specific sample has a defined buckling wavelength, suggesting that a characteristic mode of buckling exists. A theoretical prediction of the characteristic wavelength is discussed later. The wavelengths we have observed for different samples range from 300 to 700 μm, in agreement with previous studies (13). Movie 2, which is published as supporting information on the PNAS web site, shows that the contour length of MT bundles increases continuously, indicating that bundles elongate during buckling. In addition, images taken at different focal planes show that the pattern is the same. We conclude that the pattern is essentially two-dimensional.

Fig. 3.

MT bundles detected by both birefringence and fluorescence measurements. MTs polymerized from a 5 mg/ml tubulin solution in glass cuvettes were taken out and then applied on a coverslip and covered with a glass slide. (A) Results of the PolScope measurement. Brightness indicates the magnitude of retardance, and pins represent the slow axis directions that are consistent with the orientations of MT bundles. (B) Fluorescence image of the rectangular region as indicated in A.

Periodic Variations in Retardance and Fluorescence Intensity.

Both the solution retardance magnitude and the slow axis orientation of MTs vary in space (see Fig. 4A). The retardance values and the MT slow axis orientations along the white line in Fig. 4A are plotted in Fig. 4B and C, respectively. Note that the retardance is higher in the sloped regions and lower in the peak and valley regions of the waves. The periodic variation in slow axis orientation confirms the wave-like characteristic of the MT bundles that is visualized in Figs. 2 and 5A. Similar to the retardance, the fluorescence intensity undulates in space as shown in Fig. 5B.

Fig. 4.

Quantitative analysis of the striped patterns based on birefringence measurements. (A) PolScope measurement of a typical sample self-organized in 3.3 mg/ml tubulin solution (taxol-Oregon green added for fluorescence imaging performed on the same sample). The solution in a 0.4-mm-thick cuvette was initially exposed to a 9-tesla magnetic field for 30 min. The measurement was done after the pattern was stable. The brightness indicates the magnitude of retardance, and the pins show slow axis orientations. (B) Retardance values along the white line in A (blue curve) and fit (red curve) using Δ(x) = Δ₀ $\sqrt{1+{\tan }^2\varphi (x)}$. The x axis starts from the left end of the white line in A. The slow axis orientations ϕ are measured values as shown in C. The only fitting parameter is Δ₀. (C) Slow axis orientations along the same line. (D) Schematic showing that the packing density is proportional to $\sqrt{1+{\tan }^2\varphi }$ for nested MT bundles (each curve represents a bundle). (E) Retardance along the white line in A and fit proportionally to $\sqrt{1+{\tan }^2\varphi }$, where ϕ is the slow axis direction at each corresponding position.

Fig. 5.

Quantitative analysis of the striped patterns based on fluorescence measurement. (A) Phase-contrast image (contrast enhanced) of the same region as in Fig. 4 but with a smaller field of view. Blue points are manually picked up along a MT bundle. The red curve is a fit to the shape of the bundle using the sum of three sinusoidal functions. (B) Fluorescence image of the same region; the red curve is the same as in A. (C) The blue curve is a plot of the fluorescence intensity along the red curve in B as a function of the horizontal axis, x. The red curve is a fit using I(x) = I_b + I₀ $\sqrt{1+{\tan }^2\varphi (x)}$, which yields I_b = 299 and I₀ = 143. Here tanϕ(x) corresponds to the calculated slope of the contour of the bundle based on the fit to its shape. (D) Linear fit of fluorescence intensity to $\sqrt{1+{\tan }^2\varphi }$ using data from C. The nonzero intercept of the line with the ordinate implies a background fluorescence caused by dispersed MTs.

Quantitative Analysis of the Periodic Variations.

The nesting of buckled bundles accounts for the observed retardance and fluorescence intensity variations. As shown schematically in Fig. 4D, bundles of MTs buckle into a wave-like shape and nest with their neighbors. We assume that the transverse bundle displacement, S, is independent of the horizontal position, x. The local packing density of bundles (number of bundles per μm²), P, however, depends on x through ϕ(x) as:

where ϕ is the local angle of the MT bundles measured relative to the original alignment direction. As the retardance magnitude is proportional to the packing density of aligned filaments (14, 15), it is expected to follow Δ(x) = Δ₀$\sqrt{1+{\tan }^2\varphi (x)}$. To test this expectation, the measured Δ in Fig. 4B is plotted against $\sqrt{1+{\tan }^2\varphi (x)}$ in Fig. 4E. These data are consistent with the expected proportional relationship and a fit yields Δ₀ = 7.44 nm. The average retardance from these data is ≈12.1 nm, which represents the average retardance of the whole sample.

The nesting of buckled bundles also accounts for the coexisting fluorescence intensity variations. The fluorescence intensity contributed by MTs aligned in the bundles is also expected to follow I ∝ $\sqrt{1+{\tan }^2\varphi }$. Unlike the retardance, however, there is an additional background contribution, I_b, which is caused by dispersed MTs. These MTs are most likely randomly oriented as they do not contribute to birefringence. To test these expectations, we used a typical phase-contrast image (Fig. 5A) to follow the contour of a bundle [i.e., to determine ϕ(x) along the bundle]. The blue points in Fig. 5A were picked along a discernable bundle and their positions were fit to a simple Fourier expansion with three sinusoidal terms. The measured fluorescence intensities along the red fitted curve in Fig. 5B are plotted as the blue curve in Fig. 5C versus the horizontal position, x. The red curve in Fig. 5C is a fit to I(x) = I_b + I₀$\sqrt{1+{\tan }^2\varphi (x)}$, which yields I_b = 299 and I₀ = 143 (see also Fig. 5D), where I(x) is the total fluorescence intensity and tanϕ(x) is the calculated corresponding slope of the bundle based on the fit to its shape.

Fraction of MTs Aligned Along Wave-Like Bundles.

It is known that taxol binds tightly and specifically to MTs (see, for example, ref. 16). Thus the measured fluorescence signal comes mainly from MTs incorporated into bundles and in the surrounding network. To validate this assertion, we centrifuged a solution of fluorescent taxol-labeled MTs and measured the fluorescence signal of the supernatant. The signal after sedimenting MTs was <3% of the original solution (data not shown), confirming that the contribution to the fluorescence signal from free fluorescent taxol and free tubulin associated with fluorescent taxol is negligible.

Using the background and the average total fluorescence intensity, I_b and Ī, respectively, we calculated the fraction, η, of MTs incorporated into the nested bundles after the pattern became stable. For the sample presented in Fig. 5, Ī = 485 (see Fig. 5C),

where Ī − I_b is the contribution from MTs incorporated into the bundles. The fraction, η, varies with different samples. For instance, a proportion of 55% for a 5-mg/ml sample was obtained in the same way. These calculations demonstrate that only a fraction of MTs forms the striped pattern. The calculation presented next suggests that the other fraction of MTs exists in a nonbirefringent, isotropic network.

We estimate the expected average retardance for the 3.3-mg/ml sample presented in Fig. 4 and compare the estimate with the PolScope measurements. For a sample with a dimension of 24 × 8 × 0.4 mm (l × w × t), the total contour length of all of the aligned MTs in the bundles is ≈2.13 × 10¹¹ μm taking into account that the measured critical concentration is 1 mg/ml and that MTs are partially (≈38%) incorporated into the bundles. Assuming that all MTs are aligned along the long axis of the cuvette, the number of MTs passing through the cross section (w × t) is about N = 2.13 × 10¹¹ μm/24 × 8 × 0.4 mm = 2.77 × 10¹²/m². The retardance signal for a single MT has a peak of 0.07 nm at the center of the filament and decays to zero ≈0.17 μm from the center as measured by Oldenbourg and Mei (17). Thus the area under the retardance signal curve for a single MT is approximately A = 0.07 nm × 0.17 μm. Therefore the expected retardance over a 0.4-mm path length is approximately Δ = A × N × w × t/w = 13 nm, assuming that the retardance of MT bundles is the sum of the retardance of the individual constituent MTs. This estimate is in agreement with the experimental average retardance of 12.1 nm for the same solution (see Fig. 4).

Estimate of the Bundle Size.

The average number of MTs in the cross section of a bundle can also be estimated provided that the density of bundles is known. Using the fluorescence image of bundles shown in Fig. 3B we can discern on the order of 100 separate bundles spread over 150 microns. These produce an average retardance in the region (Fig. 3A) of 2 nm, presuming they dominate the retardance signal. Thus, the retardance area of a single bundle is 150 μm × 2 nm/100, which is ≈250 times the single MT value. Alternatively, we can estimate the total number of bundled MTs in the cross section of Fig. 3B (150 × 30 μm) by using the starting tubulin concentration (5 mg/ml) and presuming that only 55% of the MTs are in bundles. This process yields 31,000 MTs and thus, 310 MTs, on average, in the cross section of a bundle. Thus, the average of these estimates indicates that there are ≈280 MTs in a bundle cross section.

Discussion and Conclusion

Based on the results and analyses presented in the previous section, we propose a two-stage mechanism for the striped pattern formation: (i) polymerizing MTs align uniformly in response to magnetic torques or shear forces or other means and form bundles in the first stage; and (ii) these bundles elongate and buckle in coordination to form a nested wave-like structure in the second stage.

The spontaneous bundling of MTs without cross-linking molecules is somewhat surprising although the phenomenon has been observed previously (10). The buckling of MTs is equally surprising given that there are no force-generating motor proteins involved in our system. In the following subsections, we discuss the mechanism of bundle formation, elongation, and buckling.

Mechanism of MT Bundle Formation.

Bundling transitions of filamentous biopolymers such as DNA, F-actin, and MTs can be induced by either electrostatic or steric interaction (18). The electrostatic interaction stems from the polyelectrolyte nature of these biopolymers (18), which gives rise to nonspecific binding by ligands carrying opposite charges including counterions. At sufficiently high concentrations of counterions of appropriate valency, typically divalent or higher, a net attractive interaction can occur, leading to the subsequent lateral aggregation. The steric interaction refers to a distinct physical mechanism known also as depletion attraction to colloidal scientists or macromolecular crowding in the biochemistry literature (19). It has been theoretically predicted and experimentally shown that rigid filaments coexisting with a crowded solution of inert polymers or globular proteins may spontaneously coalesce into bundles (19, 20).

Both interactions discussed above are likely relevant to the bundle formation of MTs in this study. MTs are known to be highly negatively charged and are surrounded by counterions, particularly the divalent Mg²⁺ ions existing in millimolar concentration. The counterions significantly screen the negatively charged MTs, reducing the mutual repulsion between them. Theoretical work over the past decades has predicted attractive interactions caused by correlations of counterions shared by parallelly aligned rods of like charge (21, 22). Experimentally, MTs have been observed to form bundles in the presence of divalent and multivalent cations (23, 24). As an additional factor, unpolymerized tubulin dimers, oligomers, and even short MTs may serve as “inert” macromolecules, which facilitate the lateral aggregation of parallelly aligned MTs via the steric interaction. Indeed, MTs have been shown to form bundles of different morphologies in the presence of inert macromolecules (25).

We speculate that MT bundle formation in our system is caused by the combined effects of counterion-induced attraction and depletion force. The 2-mM divalent counterion Mg²⁺ present in the MT solutions may be insufficient to induce substantial bundling alone. Combining its effect with the depletion attraction, however, and given the fact that the polymerizing MTs are concurrently being aligned by external forces, bundling becomes the likely outcome. In fact, experimental evidence of spontaneous bundling of MTs has been given by Hitt et al. (10). In this study, we confirm the previous report and show that bundling of MTs is a key step toward developing the striated patterns.

Mechanism of Bundle Elongation and Buckling.

The bundle elongation and buckling phenomena can be qualitatively explained within the limits of the currently known force generation mechanisms in MT systems and microscopic structure of MT bundles. The occurrence of buckling implies that a longitudinal compressional stress builds up within the MT bundles. The concomitant elongation of the bundles during buckling suggests that this stress most likely results from polymerization forces exerted by individual MTs (26, 27). Other known force generation mechanisms in MT systems require molecular motors (28), which are absent from the solutions considered here. These polymerization forces can give rise to compressional stress if the MT bundles are composed of parallel MTs that are laterally packed with a spacing less than their radius of 12.5 nm. Based on the bundling discussion presented in the last section, we expect the spacing between parallel MTs to be a couple of screening lengths (see Fig. 6).

Fig. 6.

Schematic drawing illustrating the packing geometry of MTs in a bundle. (A) A longitudinal cross section of a bundle. The small dimeric molecules represent tubulin dimers. (B) A transverse cross section of a few MTs in a bundle. (C) Magnified view of the cross section of three parallel MTs in a bundle. The dotted outer circles indicate the Debye-screening layers. The spacing between adjacent parallel MTs is of the same order of magnitude as the Debye-screening length. For the ionic strength of ≈80 mM in our sample solutions, this length is ≈1.1 nm. Thus the central void made by these three MTs, assuming a hexagonal packing, is large enough for tubulin dimers to diffuse within the bundles.

The above considerations suggest a microscopic scenario that leads to bundle buckling during polymerization. We presume that as each MT in a bundle polymerizes it stays in the “track” defined by the packing of its nearest neighbors (see Fig. 6A). An individual MT elongates freely until it grows into contact with a MT occupying the same track. Upon contact, it exerts a longitudinal polymerization force on this neighboring MT rather than sliding past it. This force drives the neighbor to slide and/or creates stress in the bundle (if the neighbor is unable to slide freely). Thus, as the MTs within a bundle polymerize the bundle length increases and compressional stress builds. Once the stress exceeds a critical value, the bundle buckles. The central presumption that MTs in the same track are unlikely to slide past each other is supported by our microscopic observations. During pattern formation, bundle elongation was quite evident (see Movie 2), whereas significant bundle thickening was not observed.

We can identify parameters determining the characteristic buckling wavelength by considering the balance among mechanical energies in the system. We consider three energies: the compressional and bending energy of the bundles and the elastic energy of the background network of MTs. The buckling relieves the compression energy that builds in the bundle, but it costs energy to bend the bundle and distort the background. If we assume that the characteristic wavelength is selected at the onset of the buckling instability and thus, at the critical strain, then the system will select the wavelength that minimizes the sum of the bundle bending and network elastic energies.

Specifically, we treat the MT bundles as homogeneous elastic rods and the background network as perfectly elastic. The average bending energy per unit length of a bundle of radius R that assumes a sinusoidal wave form ξ(x) = δ sin(2πx/λ) follows, E_bend ∝ ER⁴δ²/λ⁴, where E is the Young’s modulus of the bundle. Assuming that the distortions of the elastic network are proportional to ξ(x), the average elastic energy per unit length follows, E_el ∝ αδ², where α is the elastic constant of the network sensed by the bundle per unit length. At fixed strain, which corresponds to fixed compressional energy, δ ∝ λ so that E_bend ∝ ER⁴/λ² and E_el ∝ αλ². Minimizing the energy sum with respect to λ yields λ∝$\sqrt[4]{\raisebox{1ex}{$E$}\!\left/ \!\raisebox{-1ex}{$\alpha $}\right.}$ R. This scaling result implies that λ should depend very weakly on the mechanical properties of the bundles and the network. The determination of E and α and thus, λ, however, requires techniques different from the structural characterization methods used in this study.

Alternatively, individual MTs might be able to slide freely along their neighbors so that the bending energy of the bundle may be approximated as the sum of bending each MT through the cross section (Fig. 6). Based on the flexural rigidity of a single MT of ≈34 ± 7 pN·μm² (26), the average bending energy of a MT bent in a wave-like shape with a wavelength of 600 μm and an amplitude of 300 μm is ≈0.14 k_BT/μm. The bending energy of a bundle with 280 MTs in its cross section (see Estimate of the Bundle Size) is then ≈0.14 k_BT/μm × 280 = 39.2 k_BT/μm, assuming that neighboring MTs bend independently. The actual bending energy of a bundle may be smaller than this estimate, because individual MTs with a length much smaller than the buckling wavelength do not need to bend to a large extent for the bundles to be wave-like.

In conclusion, we have shown that the microscopic structures responsible for the birefringent stripes are MT bundles that undulate in space in a wave-like manner. Concurrent undulations in the retardance and fluorescence intensity of labeled MTs are also apparent. The nesting of buckled bundles quantitatively accounts for these undulations. In addition, we show evidence that two groups of MTs exist in the system: MTs that are incorporated into the bundles and MTs that form an elastic network surrounding the bundles. The total energy of the system is minimal at the selected buckling mode that has the characteristic wavelength. The two-stage mechanism we propose for the stripe formation not only involves the chemical and biological reaction of MT polymerization and bundle formation, but also incorporates a mechanical component of the buckling of growing MT bundles. This mechanism might account for some of the global aspects of biological morphogenesis and development and provide the basis for further experimental and theoretical work.

Materials and Methods

Preparation of Tubulin.

Tubulin was isolated from bovine brain by two cycles of assembly and disassembly followed by chromatography on phosphor-cellulose (29). It was then polymerized in 1 M glutamate sodium salt following an established protocol (30). After centrifugation at 35°C, MT pellets were homogenized and resuspended in PM buffer (100 mM Pipes/1 mM EGTA/2 mM MgSO₄/0.5 mM GTP, pH 6.9), frozen in 200-μl aliquots, and stored at −80°C. We examined the purity of the tubulin preparation by Coomassie blue staining of proteins loaded (50 μg per lane) and separated on SDS/PAGE minigels, which showed no visible band other than that of tubulin. Immediately before use, tubulin solutions were thawed and then centrifuged at 1,800 × g for 5 min at 4°C to remove small amounts of aggregates. For all of our samples, the GTP concentration was 2 mM. Samples were degassed (after the addition of GTP) in cuvettes at 4°C to prevent air bubble formation that would otherwise occur during the increase in temperature to 37°C. The cuvettes were then incubated on ice for 10 min before inducing polymerization. The rectangular cuvettes have dimensions of 40 × 10 × 1 mm for quartz (International Crystals, Oklahoma City, OK) or 50 × 8 × 0.4 mm for glass (Vitrocom, New Bedford, MA).

Aligning MTs with Static Magnetic Fields.

The application of static magnetic fields has been a nonintrusive mechanical method to align biological samples (31–34). In particular, the alignment of MTs in a magnetic field of a few tesla has been shown by Glade and Tabony (13). Theoretical estimation shows that the minimum field strength needed to align a 5-μm MT parallel to the magnetic field direction is ≈7.6 tesla (31). For MTs >5 μm, the required field strength is even smaller. The magnetic field in our experiments was produced by a superconducting magnet system (American Magnetics, Oak Ridge, TN) with a room temperature bore. The diameter of the bore was 11 mm. Precooled tubulin solutions in glass cuvettes were placed in a 9-tesla vertical magnetic field oriented parallel to the long axis of the cuvettes. The temperature of the bore was preequilibrated to 37°C by circulating warm air through it from above. The sample temperature, measured with a thermometer, rose from 0°C to 37°C in ≈100 s. Observations and measurements were made at either room temperature or 30°C, when specified, after the sample was removed from the magnet.

Fluorescence and Phase-Contrast Microscopy.

Microscopic structures of self-organized samples inside cuvettes were examined with fluorescence and phase-contrast microscopy at room temperature on a Nikon ECLIPSE E800 microscope. Images of 12-bit depth were collected by a 1,392 × 1,040-element Coolsnap digital camera (Roper Scientific, Trenton, NJ) driven by metamorph imaging software (Universal Imaging, Downingtown, PA). For fluorescence imaging, MTs were labeled to 3.5% in the ratio of total number of Oregon green-conjugated taxol (taxol-Oregon green) (Molecular Probes) molecules to tubulin dimers. Blue light (wavelength 480 nm) was used for excitation, and the green light emitted by taxol-Oregon green (wavelength ≈532 nm) was measured.

Birefringence Measurements.

One easy and quick method to examine sample birefringence is to place the cuvette between two sheets of polarizing film (Edmund Optics, Blackwood, NJ) oriented with their axes of transmission at 90° (extinction 99.98%) and illuminated by a light box (Hall Productions, Grover Beach, CA). Eight-bit depth images were recorded by a charge-coupled device camera (XCD-SX900; Sony) driven by fire-i software at a resolution of 1,280 × 1,024.

More quantitative birefringence measurements were performed with a Nikon ECLIPSE E800 microscope equipped with a PolScope package (CRI, Cambridge, MA) and a standard charge-coupled device camera (MTI 300RC; Dage–MTI, Michigan City, IN) with 640 × 480 resolution. This system produces images of the retardance and slow axis (for MTs, this is the long axis of the filaments) orientation of birefringent samples (35). Strain-free objectives were used.

Sedimentation and Quantitative Fluorescence Assay.

This assay was performed to test the contribution of free fluorescent taxol and free tubulin associated with taxol to the total fluorescence signal. First, the fluorescence of a solution of fluorescent taxol labeled (with a stoichiometry of 3.5% in the ratio of the total number of taxol molecules to that of tubulin dimers) MTs was measured with a fluorescence spectrometer (PerkinElmer). Then the solution was centrifuged at 280,000 × g for 30 min to sediment MTs. The fluorescence of the supernatant was subsequently measured.

Abbreviation

MT

microtubule.